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edu:topics:complex:start [2017/11/10 15:16] simon |
edu:topics:complex:start [2018/02/21 23:51] (current) simon [notes] |
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√ −1, instead of being | √ −1, instead of being | ||
called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity. | called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity. | ||
+ | </quote></quote> | ||
+ | |||
+ | ---- | ||
+ | just like calculus was re-defined in terms of limits to eliminate "impossible" infinities, so | ||
+ | complex numbers are redefined considering groups and sets ... but this requires a great deal more theory: | ||
+ | <quote></quote>http://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf<quote> | ||
+ | Augustin-Louis Cauchy (1789-1857) initiated complex function theory in an 1814 memoir | ||
+ | submitted to the French Acad´emie des Sciences. The term analytic function was not | ||
+ | mentioned in his memoir, but the concept is there. The memoir was published in 1825. | ||
+ | Contour integrals appear in the memoir, but this is not a first, apparently Poisson had | ||
+ | a 1820 paper with a path not on the real line. Cauchy constructed the set of complex | ||
+ | numbers in 1847 as R[x]/(x2 + 1) | ||
+ | <quote>We completely repudiate the symbol √ | ||
+ | −1, abandoning it without regret because | ||
+ | we do not know what this alleged symbolism signifies nor what meaning | ||
+ | to give to it. | ||
</quote></quote> | </quote></quote> | ||
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====notes==== | ====notes==== | ||
- | [[edu:resources:schrodinger-life]] | [[edu:resources:gleick-chaos]] | galileo | | + | [[books:schrodinger]] | [[edu:resources:gleick-chaos]] | galileo | |
copernicus | [[edu:resources:penrose-physics]] | copernicus | [[edu:resources:penrose-physics]] | ||